Sutton, who also scored the opener, nudged the ball home at the far post when he raced onto Lionel Ainsworth's low cross in the dying seconds.
And it was a point the hosts thoroughly deserved in an end-to-end contest which saw Motherwell take a two-goal advantage only for the champions to battle back and briefly hold the lead themselves.
Both keepers made vital saves, while Celtic also missed a first-half penalty when they were 1-0 down.
The hosts had needed less than four minutes to open the scoring when Sutton collected Stephen McManus' long punt forward before netting from a tight angle, although keeper Fraser Forster will feel he should have done better than just deflect the ball into the bottom corner of the net.
Henri Anier missed a great chance to add a second on the break after Baram Kayal had stumbled and lost the ball in the Motherwell half.
Celtic then missed a superb opportunity to level matters in the 21st minute when Iain Vigurs bundled over Anthony Stokes in the box and referee Craig Thomson pointed at the spot.
However, Kris Commons suffered his first failure in 10 attempts although keeper Gunnar Nielsen must be given the credit for palming away a well-struck and well-directed shot.
Steven Hammell denied Celtic a definite equaliser as he cut out a Stokes cross with Kris Commons standing unmarked at the far post for what would have been a simple tap-in.
And the hosts doubled their lead two minutes before the break when the burly Zaine Francis-Angol was in the right place to turn the ball home from close range.
But just seconds before the break Stokes remained calm under pressure as he hooked the ball home from a tight angle inside the box, leaving keeper Nielsen with no chance of preventing Celtic's first goal.
Although the Hoops started the second half strongly, they could have conceded a third goal on 54 when Kayal nodded off his own line from Fraser Kerr's header.
And less than 60 seconds later, Celtic were level through Georgios Samaras who clipped home from close range after latching onto a Stokes assist following a Commons corner.
Nielsen then made a brilliant save to deny Scott Brown on 65, while Celtic keeper Forster did likewise to push away Anier's fierce shot on the turn in the 82nd minute.
With just five minutes remaining, substitute Leigh Griffiths appeared to have won the game for Celtic when the striker cooly found the bottom right-hand corner of the net from 15 yards.
But Motherwell hit back on the break with Sutton claiming his second goal of the match to move his team within one point of second placed Aberdeen who they meet on the final day of the season.